Question

the given graph show the displacement versus time relation for a disturbance travelling with a velocity of 10 metre per second calculate the time period frequency wavelength of a disturbance​

Answer 1

$\huge{\bold{\underline{\underline{....Answer....}}}}$

$\huge{\bold{\underline{Given:-}}}$

• Velocity (v) = 10 m/s.

$\huge{\bold{\underline{Explanation:-}}}$

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Time taken to complete one cycle is 2 seconds.

(As the it comples one wave in 2 seconds)

Now, From relation,

$\large{\boxed{\tt v = \nu \lambda}}$

where,

• v = Velocity of Disturbance
• ν = Frequency
• λ = Wavelength,

Before That Finding the frequency,

$\large{\boxed{\tt \nu = \dfrac{1}{T}}}$

Substituting the values,

$\large{\tt \nu = \dfrac{1}{2}}$

$\large{\boxed{\tt \nu = 0.5 \: Hz}}$

$\rule{300}{1.5}$

$\rule{300}{1.5}$

$\large{\boxed{\tt v = \nu \lambda}}$

Rewriting the equation,

$\large{\tt \lambda = \dfrac{v}{\nu}}$

Substituting the values,

$\large{\tt \lambda = \dfrac{10}{0.5}}$

$\large{\tt \lambda = \dfrac{10 \times 10}{5}}$

$\large{\tt \lambda = \dfrac{\cancel{10} \times 10}{\cancel{5}}}$

$\large{\tt \lambda = 10 \times 2}$

$\huge{\boxed{\boxed{\tt \lambda = 20 \: meters}}}$

So, the Wavelength of Disturbance is 20 meters.

$\rule{300}{1.5}$

Answer 2

Question :-

the given graph show the displacement versus time relation for a disturbance travelling with a velocity of 10 metre per second calculate the time period frequency wavelength of a disturbance.

Answer:-

→ Wavelength is 20 m.

To Find :-

Find the wavelength.

Formula used :-

$\star \: \text{time \: peroid} \: = \frac{1}{ \text{frequency} } \\ \\ \star \: \text{v \: } = \nu \: \: \lambda \: \: \\ \implies \: \text{ v \: is \: the \: velocity }\: \\ \implies \: \nu \: \text{is \: frequency} \\ \implies \: \lambda \: \text{ is \: wavelength \: }$

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Explanation :-

Given that,

• Velocity (v) = 10 m/s

• Time taken in one complete cycle (t) = 2 second

We know that,

$\implies \: t \: = \frac{1}{ \nu} \\ \\ \implies \: 2 = \frac{1}{ \nu} \\ \\ \implies \: \boxed{\nu \: = \frac{1}{2} = 0.5}$

Now ,

Using the given formula ,

$\implies \: \text{ v \:} = \nu \: \lambda \:$

substitute the above values,

$\implies \: 10 = \: 0.5 \: \times \lambda \\ \\ \implies \: \lambda \: = \frac{10}{0.5} \\ \\ \implies \: \boxed{\lambda \: = 20 \: } \: \: {m}$

Therefore the wavelength is 20 m.

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